Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian random field whose components are independent and satisfy some mild conditions.We study the packing dimension of range X(E)under the anisotropi...Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian random field whose components are independent and satisfy some mild conditions.We study the packing dimension of range X(E)under the anisotropic(time variable)metric space(R^(N),ρ)and(space variable)metric space(R^(d),τ),where E⊂R^(N) is a Borel set.Our results generalize the corresponding results of Estrade,Wu and Xiao(Commun.Stoch.Anal.,5,41-64(2011))for time-anisotropic Gaussian random fields to space-time anisotropic Gaussian fields.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11971432)Natural Science Foundation of Zhejiang Province(Grant No.LY21G010003)+2 种基金Humanities and Social Sciences Foundation of the Ministry of Education(Grant No.18YJA910001)First Class Discipline of Zhejiang-A(Zhejiang Gongshang University-Statistics)Natural Science Foundation of Chuzhou University(Grant No.zrjz2019012)。
文摘Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian random field whose components are independent and satisfy some mild conditions.We study the packing dimension of range X(E)under the anisotropic(time variable)metric space(R^(N),ρ)and(space variable)metric space(R^(d),τ),where E⊂R^(N) is a Borel set.Our results generalize the corresponding results of Estrade,Wu and Xiao(Commun.Stoch.Anal.,5,41-64(2011))for time-anisotropic Gaussian random fields to space-time anisotropic Gaussian fields.
